Less serious than getting together or dating. Spending time with someone in the context of friendship or in the context of casually exploring whether you like someone as just a friend or maybe more than a friend.

I'm gonna hang out with my best friend this weekend. We should hang out some time.

The Urban Dictionary Mug

Comes from the formal meaning of "hang out": to protrude or stick out. Hence, the use of "out" for public. Not to be confused with "hang with", which is an umbrella term that includes socializing publicly or privately.

Friend: "Dude, you never hang out with me anymore."
You: "Not true: even though I don't get out of my house much, I still socialize with you on Facebook, which can be seen by other people."
Friend: "Touché."